How do I fix this irregular shading on my subsurf retopology attempt?
you have nGons which tends to cause problems for both sub-division modifiers, animations and texture baking. 

For hard-surface/mechanical type models, you can use tris/nGons on flat areas so long as the transitions to curved areas are all bordered with quad based geometry.  Note this will still make some of the selection tools less effective.



The following chart shows many ways of redirecting polygon flow so you can keep an all-quads mesh that has clean lines that will still work well with various modeling tools.  



Credits: The authors name can be seen at the bottom of the image.  

I have found half a dozen charts like this so you might want to do some more digging using keywords such as "polygon flow" "quad modeling" as the basis for an image search.